Nonhomogeneous Dirichlet problems without the Ambrosetti-Rabinowitz condition
ID Li, Gang (Avtor), ID Rǎdulescu, Vicenţiu (Avtor), ID Repovš, Dušan (Avtor), ID Zhang, Qihu (Avtor)

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Izvleček
We consider the existence of solutions of the following ▫$p(x)$▫-Laplacian Dirichlet problem without the Ambrosetti-Rabinowitz condition: ▫$$\begin{cases} -\text{div} \, (|\nabla u|^{p(x)-2}\nabla u) = f(x,u) & \text{ in } \quad \Omega , \\ u=0 & \text{ on } \quad \partial \Omega . \end{cases}$$▫ We give a new growth condition and we point out its importance for checking the Cerami compactness condition. We prove the existence of solutions of the above problem via the critical point theory, and also provide some multiplicity properties. The present paper extend previous results of Q. Zhang and C. Zhao (Existence of strong solutions of a ▫$p(x)$▫-Laplacian Dirichlet problem without the Ambrosetti-Rabinowitz condition, Computers and Mathematics with Applications, 2015) and we establish the existence of solutions under weaker hypotheses on the nonlinear term.

Jezik: Angleški jezik nonhomogeneous differential operator, Ambrosetti-Rabinowitz condition, Cerami compactness condition, Sobolev space with variable exponent Članek v reviji (dk_c) 1.01 - Izvirni znanstveni članek PEF - Pedagoška fakultetaFMF - Fakulteta za matematiko in fiziko 2018 Str. 55-77 Vol. 51, no. 1 517.956.2 1230-3429 10.12775/TMNA.2017.037 18162521 29.08.2019 541 370 AddThis uporablja piškotke, za katere potrebujemo vaše privoljenje.Uredi privoljenje...